5421 ÷ 7 = 774 R3
Alright, let's work through the division of 5421 by 7 step by step.

Step 1:
7 goes into 5 0 times with a remainder of 5.
Write down 0 as next digit of of the result. 
Result so far: 0
Subtract 0 from 5 to get 5.
Bring next digit (4) of the dividend behind the 5 and repeat the process: 54 / 7

Step 2:
7 goes into 54 7 times with a remainder of 5.
Write down 7 as next digit of of the result. 
Result so far: 7
Subtract 49 from 54 to get 5.
Bring next digit (2) of the dividend behind the 5 and repeat the process: 52 / 7

Step 3:
7 goes into 52 7 times with a remainder of 3.
Write down 7 as next digit of of the result. 
Result so far: 77
Subtract 49 from 52 to get 3.
Bring next digit (1) of the dividend behind the 3 and repeat the process: 31 / 7

Step 4:
7 goes into 31 4 times with a remainder of 3.
Write down 4 as next digit of of the result. 
Result so far: 774
Subtract 28 from 31 to get 3.

The final result is 774 with a remainder of 3.